PS5 and the subtle difference between backward compatibility and continuity

Will PlayStation 5 allow you to play games of past generations? And if so, which ones? Lately this question has re-emerged the debate around the importance of the backward compatibility of a platform. However, many seem to confuse backward compatibility with the idea of ​​continuity, two very similar and at the same time very different concepts, which have only recently crossed their paths. With Sony continuing to clarify the PS5 approach, complaints and underestimations mix with each other creating extreme confusion and this is bad because the battles, the right ones, must be faced together. Shall we start to do some order?